Research on the Spatial Density Algorithm of Space Debris

With the development of human's space technology and activities, the space debris environment is getting more and more deteriorated, which results in a great threat to the safety of on-orbit space vehicles. Due to the threat, it's necessary to establish an engineering model for the space debris environment to access space vehicle's impact risk. Since the spatial density is the most important component in an engineering model of space debris environment, this paper is devoted to study the algorithm of the spatial density of space debris. By introducing the orbital parameters, the paper firstly gives the conception and the mathematical definition of spatial density of space debris. According to the definition, construction of the spatial density is carried out. With the aid of probability theory and orbital mechanics, the paper theoretically derives a general analytical expression for the spatial density. Afterwards, simplification of the general expression is discussed by introducing some assumptions, i.e., uniform distribution over right ascension of the ascending node and over the perigee argument, independence of orbital parameters and of spatial coordinates. The result is a more simplified expression of the spatial density, which is suitable for computation. It turns out that the SDPA model's algorithm is just a particular case of the paper's general expression. To enlarge the simplified result's for application, the paper proposes the classification method. To verify the paper's result, application to the Two-line elements is presented, which validates the paper's result. The application also shows that the classification method can help to improve accuracy.